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From: Steven Watanabe (steven_at_[hidden])
Date: 2007-03-28 16:10:40


Noah Roberts <roberts.noah <at>> writes:

> Steven Watanabe wrote:
> > I may be wrong, but in order to avoid any excess loss
> > of precision you have to store a set of all the base
> > units and track the actual unit at runtime involving
> > a merge with every multiplyor divide. This kind of
> > overhead is not always acceptable.
> I don't understand what you are saying.

suppose that you store the actual value and the
conversion factor.

struct quantity {
    double conversion_factor;
    double value;

Now multiplying two quantities requires two
multiplications. Alternately, you convert
to SI before doing the multiplication and
return a different type. Either way you
introduce extra operations thus reducing
the precision of the result.

The only way I can think of to enable runtime
units without losing precision is

struct base_unit {
    double conversion_factor;
struct unit_impl {
    typedef boost::rational exponent_t;
    //keep this sorted to allow merge
    std::vector<std::pair<base_unit*, exponent_t> > impl;
    double conversion_factor;
static std::set<unit_impl*> all_units;

typedef boost::shared_pointer<unit_impl> unit;

struct quantity {
    unit u;
    double value;

Now all unit multiplications add the exponents of identical
dimensions. Every time you create a new unit you look it up
see whether an identical unit has already been created. If
so than you return a pointer to the existing unit. This
is so that you can explicitly set the conversion factors
for complex units and thus get maybe another bit of precision.

> I've never seen that stated. I don't believe it either. If conversions
> are not the point of the library than why is a very significant portion
> of the library dealing with units and conversions?

A lot of code is dedicated to conversions because they are
rather difficult to implement given the current representation.
Most of it is in detail/conversion_impl.hpp which is highly
repetitious. If I ever get around to simplifying it the portion
of the library dealing with it will appear much smaller.

In Christ,
Steven Watanabe

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